Question

How do you find the length of a triangle's sides using only its angles: 35, 65, 80 and the area is 4000?

Answer 1

In `DeltaABC`, the area is given by `A = 1/2ab sin C`. We let the sides be `a`, `b` and `c`. Hence, we write a system of equations in three variables to describe the situation.

`4000 = 1/2ab sin(35)`

`4000 = 1/2bc sin(65)`

`4000 = 1/2ac sin(80)`

We use a graphing calculator or C.A.S (Computer Algebra System) to solve.

We get: `a ~= 113.295`, `b~= 123.108` and `c~= 71.7013`

Hopefully this helps!